Water-richness evaluation method and application of clastic rock aquifer in mining seam roof

Clastic rock aquifer of the coal seam roof often constitutes the direct water-filling aquifer of the coal seam and its water-richness is closely related to the risk of roof water inrush. Therefore, the evaluation of the water-richness of clastic rock aquifer is the basic work of coal seam roof water disaster prevention. This article took the 4th coal seam in Huafeng mine field as an example. It combined the empirical formula method and generalized regression neural network (GRNN) to calculate the development height of water-conducting fracture zone, determined the vertical spatial range of water-richness evaluation. Depth of the sandstone floor, brittle rock ratio, lithological structure index, fault strength index, and fault intersections and endpoints density were selected as the main controlling factors. A combination weighting method based on the analytic hierarchy process (AHP), rough set theory (RS), and minimum deviation method (MD) was proposed to determine the weight of the main controlling factors. Introduced the theory of unascertained measures and confidence recognition criteria to construct an evaluation model for the water-richness of clastic rock aquifers, the study area was divided into three zones: relatively weak water-richness zones, medium water-richness zones, and relatively strong water-richness zones. By comparing with the water inrush points and the water inflow of workfaces, the evaluation model's water yield zoning was consistent with the actual situation, and the prediction effect was good. This provided a new idea for the evaluation of the water-richness of the clastic rock aquifer on the roof of the mining coal seam.

www.nature.com/scientificreports/This method involves in-depth exploration of hydrogeological exploration data, selecting and weighting factors affecting water-richness, and constructing a water-richness evaluation model based on statistical or fuzzy mathematical methods, it comprehensively considers the weights of various influencing factors and indicators, and the zoning results obtained can truly reflect the characteristics of aquifer water-richness 9 .Currently, it is the most widely used method, but the degree of hydrogeological exploration in most coal mining areas in China is relatively low, and the unit water inflow data of aquifers is limited, which cannot fully reflect the distribution characteristics of aquifers.In addition, some scholars had a relatively single method for weighting impact indicators, which affects the accuracy of water-richness evaluation 10 .
Through comprehensive comparison of the above-mentioned methods for evaluating the water-richness of the coal seam roof, this study decided to use the multi-factor comprehensive analysis method.The main idea of the multi-factor comprehensive analysis method is to first establish an index system for the indicators influencing water-richness, and then couple the indicators with their weights to establish an evaluation model.Yu et al. 11 determined the weights of aquifer influencing factors using Analytical Hierarchy Process (AHP) and conducted water-richness zoning using SURFER software.Tang et al. 12 combined AHP with entropy weight method and established an evaluation model using ArcGIS software, which yielded reliable results.Bi et al. 13 combined AHP with independent weight coefficient method to establish an evaluation model with high accuracy.Wang et al. 14 also used AHP to establish an evaluation system and conducted water-richness zoning in the study area, providing scientific guidance for the prevention and control of water disasters in mining areas.Qiu et al. 15 successfully applied Fuzzy Delphi Analytic Hierarchy Process (FDAHP) combined with entropy weight method, introducing the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method to construct an aquifer richness evaluation model.In another study area, Qiu et al. 5 combined FDAHP with grey correlation analysis to establish a water-richness zoning model with high accuracy.Huang et al. 10 combined FDAHP with entropy weight method to establish a water-richness zoning evaluation model through the theory of unascertained measures, and the model has certain reliability.Li et al. 16 and Gong et al. 17 applied Back-Propagation neural network (BP) in aquifer richness evaluation, summarizing the distribution pattern of aquifer richness and achieving accurate prediction.Li et al. 18 used random forest to establish a model and evaluate the weights of various influencing indicators, conducting zoning of water-richness in the study area, with results meeting the accuracy requirements.Some scholars only used one weighting method, and the obtained weights may be too subjective or objective; Some scholars had also adopted various weighting methods but only used simple geometric averaging to combine weights, lacking scientific rigor.So how to balance the influence of subjective and objective weights and improve the accuracy of weights has become an urgent problem to be solved.
This article took the 4th coal seam in Huafeng mine field as the research object.Firstly, the Generalized Regression Neural Network (GRNN) and the "three down" regulation formula were comprehensively used to calculate the development height of the water-conducting fracture zone in the coal seam roof, to more accurately determine the vertical spatial range of water-richness evaluation.On this basis, the analysis was conducted from two aspects: lithological structural characteristics and structural development characteristics.Lithological structural characteristics refer to the intrinsic properties of the rock itself, including its composition and internal structure, manifested as rock type, rock structure, thickness of sandstone layer, etc. Structural development characteristics refer to the changes in geological structure and geomorphological formations caused by geodynamic effects, manifested as the development of folds and faults formations.The depth of the sandstone floor, brittle rock ratio, lithological structural index, fault strength index, fault intersections and endpoints density were selected as the main controlling factors to evaluate the water-richness of the clastic rock aquifer in the study area.Based on the minimum deviation method, the main controlling factors' subjective and objective weights obtained from Analytic Hierarchy Process (AHP) and Conditional Entropy Improved Rough Set Theory were effectively fused to obtain comprehensive weights, making the weight results more reasonable.Introducing the theory of unascertained measurement and confidence criteria, a water-richness evaluation model for the clastic rock aquifer of the 4th coal seam roof in Huafeng Coalfield was constructed.Compared with the water inrush points and the water inflow of some workfaces in the mine, the zoning prediction results of the evaluation model were relatively consistent.The method in this article provided a new approach for evaluating the water-richness of clastic rock aquifers in coal seam roof during mining.

Overview of geological structure
Huafeng mine field lies in Huafeng Town, Ningyang County, Shandong Province, China.The site lies between 117° 07′ 28″ E and 117° 11′ 11″ E longitude and 35° 51′ 49″ N and 35° 54′ 52″ N latitude.The Huafeng mine field is a fault block depression bounded by faults on three sides, namely the east, north, and west.It is generally a dustpan shaped syncline structure that plunges towards the northeast, with a dip angle of 17° to 40°.The structure of the mine field is relatively simple (Fig. 1).Local normal faults with a drop of no more than 30 m and a few reverse faults have developed in the mine field, which generally extend relatively short and tip out towards the deep.In addition, multiple secondary folds have also developed in the mine field.However, except for the two obvious synclines at the turning points of the two wings, the scale is generally very small, and the deformation towards the deep is unusually gentle and even disappears.The strata in the study area include the Middle Lower Ordovician, Carboniferous Yuemengou Group Benxi Formation, Carboniferous Permian Yuemengou Group Taiyuan Formation, Permian Yuemengou Group Shanxi Formation, Permian Shihezi Formation, Paleogene Lower Guanzhuang Group, and Quaternary System.The main coal bearing strata have a total thickness of 325.86 m and a total of 24 coal layers.The Shanxi and Taiyuan formations are the main coal bearing strata.

Data and method
The evaluation of the water-richness of the clastic rock aquifer on the roof of the mining coal seam mainly included the following steps: (1) By using empirical formulas and GRNN neural networks, the height of the development of water-conducting fracture zones above coal seams was calculated.(2) Based on the multi-factor control mechanism of water-richness in the coal seam roof and hydrogeological data of the study area, the main controlling factors of the water-richness in the clastic rock aquifer above the mining coal seam were selected.(3)  The AHP method and the rough set theory improved by conditional entropy were used to calculate the subjective and objective weights of each main controlling factor, and comprehensive weight was obtained based on the minimum deviation.(4) The evaluation model of water-richness was established for the study area using the theory of uncertain measurement and confidence criteria.The water-richness of clastic rock aquifer above the coal seam was analyzed, and a grading prediction was made (Fig. 3).

Prediction of the development height of water-conducting fracture zones
After coal seam mining, the overlying rock above the goaf undergoes damage and deformation.According to the "upper three zones" theory of coal mining, the areas of damage and deformation are divided into caving zone, fractured zone, and bending subsidence zone.Among them, the caving zone and fractured zone are collectively referred to as water-conducting fracture zone.(Fig. 4) The water-conducting fracture zone connects the clastic rock aquifer on the coal seam roof with the workface.The clastic rock aquifer within this height range constitutes the direct water-filling aquifer for water inrush on the coal seam roof, and the water-conducting fracture zone becomes the main channel for water damage on the coal seam roof.It is of great significance for the safe mining

Empirical formula method
At present, on-site technical personnel in coal mines in China widely use the formula provided in the "Regulations on the Retaining and Mining of Coal Pillars in Buildings, Water Bodies, Railways, and Main Tunnels" 19 to calculate the development height of water-conducting fracture zones.In the regulations, based on the size of uniaxial compressive strength, the roof lithology is divided into four types: hard, medium-hard, weak, and extremely weak, and different formulas are used according to the degree of hardness 20 .
The calculation formula for the development height of water-conducting fracture zones with different lithology is as follows:  www.nature.com/scientificreports/where∑M is the total thickness of coal seam mining, in meters, and H is the height of water-conducting fracture zone, in meters.
The empirical formula method is simple and fast, but only considers the strength of coal seam overlying rock and mining thickness, and the specific geological and mining conditions of different workfaces are not the same.Therefore, the predicted values obtained by this method are only for reference and need to be further analyzed in conjunction with other methods.

Neural network method
With the development of computer technology, neural networks have been widely used for predicting the development height of water-conducting fracture zones.Its advantage is that it can process a large amount of data, extract useful features from it, and better identify trends related to the height of hydraulic fracture zones.A trained neural network model can be used for online prediction in actual production processes, which means it can predict real-time data, assist in practical applications, and adjust and optimize accordingly.
Generalized regression neural network (GRNN) is a type of Radial Basis Function Neural Network (RBF) that has been widely used in the field of regression prediction.It has stronger approximation ability and learning speed compared to RBF networks, strong nonlinear mapping ability, and learning speed, and simple structure with single parameter setting 21,22 .
(1) Input layers: the number of input neurons is equal to the dimension of the input vector in the training sample, and the input neurons directly enter the next pattern layer.(2) Pattern layers: the number of neurons in the pattern layer is equal to the number of neurons in the input layer, and non-linear transformation is performed on the output from the input layer.The transfer function of the i neuron is often used as follows: where P i is output layer neuron model; X is input vector for the network; X i is a learning sample for the corresponding i neuron; σ is the smoothing factor; n is the number of training samples.
(1)  (3) Sum layers: this layer is used to calculate the total output from the pattern layer, and there are two types of neurons applied to it.
The first neuron algorithm adds all neurons in the pattern layer, with a connection weight of 1 between each neuron in the pattern layer and the transfer function is: Another calculation formula has added weighted sum, where the j element in the i output sample Y i is the connection weight between the i neuron in the pattern layer and the j element in the summation layer and the neuron.Its transfer function is: where Y i is the i output sample; n is the number of nodes in the pattern layer; k is the dimension of output vector; Y ij is the j value of the result vector in the i training sample.
S D as the denominator of the output layer, this function is mainly used for normalization to ensure the stability of the output results, its calculation is relatively simple, and can avoid the numerical instability caused by the molecular part of the value is too large.S N j as the molecule of the output layer, by weighting the contribution of each sample, this function is able to more accurately reflect the similarity between the input vectors and the training samples, thus improving the accuracy of the prediction.
(4) Output layers: the number of neurons in the output layer is equal to the dimension k of the output vector in the training sample, and the output result of each neuron is: where y i is the output of the j node in the output layer, which is the predicted result.
The GRNN neural network will be trained by the measured cases of the development of water-conducting fracture zones with similar geological conditions to the study area.Suitable influencing factors need to be selected as input values for the input layer.Based on the drilling data and previous studies in the research area, four factors, namely coal seam thickness, proportion coefficient of hard rock lithology, dip length of the workface, and mining depth, were selected as the influencing factors for the development height of the water-conducting fractured zone.a. Coal seam thickness (m).This factor plays a crucial role in determining the development height and serves as the primary controlling factor for determining the conduit height in traditional empirical formulas.With increasing coal seam thickness, the caving zone expands, leading to a corresponding increase in the development of the water-conducting fractured zone.b.Proportion coefficient of hard rock lithology (b) 15 .This factor can replace the two influencing factors of the uniaxial compressive strength and structural type of the roof combination rock layer, reflecting the strength type and lithology combination of the coal seam roof.c.Dip length of the workface (l).Prior to the full exploitation of coal seams, the dip length of the workface has a significant impact on the development of the water-conducting fractured zone, with the development height increasing as the workface advances.After the coal seam has been fully exploited, the effect of the dip length of the workface on the development of the fractured zone is not significant.
(6) www.nature.com/scientificreports/d.Mining depth (s).As the mining depth increases, the mine pressure also increases, causing previously unconnected fractures in the overlying strata of the coal seam to become interconnected, thus forming water-conducting channels.Therefore, mining depth can be considered as a influencing factor.
After the training of the GRNN neural network was completed by the measured data, the above influencing factors were substituted into the network as the input layer data, and the predicted value of the height of the development of the water-conducting fracture zone in the roof of the coal seam in the study area could be obtained.

Analysis of the main controlling factors of water-richness
The selection of the main controlling factors of the coal seam roof aquifer is the prerequisite and foundation for the evaluation of water-richness.Reasonable selection of the main controlling factors can greatly improve the scientific and reliable evaluation of the water-richness of the coal seam roof aquifer.Based on the hydrogeological data of the study area, this article selected the depth of the sandstone floor, brittle rock ratio, lithological structure index, fault strength index, fault intersections and endpoints density as the main controlling factors for evaluating the water-richness of the clastic rock aquifer on the roof of the 4th coal seam in Huafeng mine field.a. Depth of the sandstone floor (D), is the bottom burial depth of the sandstone in the upper part of the mining coal seam.The main impact of this factor is that as the depth increases, the static pressure of the rock will also gradually increase, and the degree of compaction of the sandstone will also increase.This will reduce the probability of cracks in the rock layer and reduce the water-richness 27 .b. Brittle rock ratio (R), is the ratio of brittle rock thickness to plastic rock thickness within the statistical range.
National and international scholars have evaluated the brittleness of rocks from different perspectives, such as mineral composition 28 , stress-strain curves based on rock brittleness characteristics 29 , and rock mechanics parameters 30 .In this study, the brittleness of rocks is analyzed based on the rock mechanics parameters and mineral composition of each stratum in the coal seam roof.
From the analysis of rock mechanics parameters, combined with the preliminary geological survey report of the study area, the brittleness of rocks is quantified by calculating the area enclosed by the uniaxial tensileuniaxial compressive strength curve 28 .The formula is shown below: where B is the brittleness of the rock, σ c is the uniaxial compressive strength of the rock, σ t is the uniaxial tensile strength of the rock.The rock mechanics parameters and brittleness degree of the roof strata of the 4th coal seam in Huafeng coal mine are shown in Table 1.
In terms of rock mineral composition, conglomerate, coarse-grained sandstone, medium-grained sandstone, and fine-grained sandstone in the strata often contain brittle minerals such as quartz, while siltstone and mudstone commonly contain clay minerals.
Taking all factors into consideration, we classified fine-grained sandstone, medium-grained sandstone, coarsegrained sandstone, and conglomerate as brittle rocks, while classifying siltstone and mudstone as plastic rocks.
Compared to plastic rocks, brittle rocks are more prone to generating a large number of cracks under stress, greatly enhancing their water permeability and storage capacity.Therefore, the brittle rock ratio can be used as a factor affecting the water-richness of aquifers, and the larger the ratio, the stronger the water-richness of aquifers 11 .The formula for calculating the brittle rock ratio is as follows: where R is the brittle rock ratio; a is the thickness of conglomerate and coarse-grained sandstone, in meters; b, c is the thickness of medium-grained sandstone and fine-grained sandstone, in meters; d is the thickness of plastic rocks such as siltstone and mudstone, in meters.c.Lithological structure index (L).Using this factor to reflect the lithology, thickness, and combination characteristics of sand and mudstone within the range of water-conducting fracture zones, the larger the lithological structure index, the better the water-richness of the aquifer.The calculation method of lithological structure The thickness of fine-grained sandstone, medium-grained sandstone, conglomerate, etc., is multiplied by an equivalent coefficient to convert it into the thickness of coarse-grained sandstone, and then multiplied by the structural coefficient 31 .The structural coefficient refers to the coefficient determined by the sand-mud combination structure of the rock layer.The structural coefficients are taken as shown in Table 2.
The formula for calculating the lithological structure index is as follows: where L is the lithological structure index; a is the thickness of conglomerate and coarse-grained sandstone, in meters; b, c is the thickness of medium-grained sandstone and fine-grained sandstone, in meters; g is the structural coefficient.
d. Fault strength index (I).Faults provide storage space and migration channels for groundwater, connecting coal seams and roof aquifers, and are important factors causing water inrush from coal seam roof aquifers.The fault strength index, which combines the fault drop, horizontal extension length, and number of faults, can quantitatively evaluate the development of faults and objectively and truly reflect the complexity of faults.
The formula is 32 : where I is the fault strength index; n is the total number of faults per grid; H i is the drop of the I fault in a certain grid, in meters; L i is the length of the I fault in a certain grid, in meters; i = 1, 2, …, n; S is grid area, in square meters.e. Fault intersections and endpoints density (F).At the intersections and endpoints of faults, due to stress concentration and the cutting effect between faults, the degree of rock fracture is greater and the cracks are more developed, increasing the possibility of water inrush from the coal seam floor.Fault intersections and endpoints density is the sum of fault intersections and pinch points per unit area divided by the area of the area, which can intuitively reflect the complexity of the fault, the formula is as follows: where F is the fault intersections and endpoints density; n is the total number of intersections and endpoints of all faults in the grid; S is grid area, in square meters.
By conducting statistics and analysis on the existing drilling data and geological data exposed in the Huafeng mine field, the Golden Software Surfer software was used to draw thematic maps of various main control factors, as shown in Fig. 6:

Calculation of weight of main controlling factors
The weight of the main controlling factors plays a crucial role in accurately determining the evaluation results when conducting a multi-factor coupling evaluation of the water-richness of the coal seam roof aquifer.In traditional methods, weighting methods are too single, subjective or objective, or only use simple geometric averaging methods, which do not effectively combine subjective and objective weights, affecting the accuracy of weights.This article used the rough set theory method improved by conditional entropy and AHP to calculate subjective and objective weights respectively, and then effectively combined subjective and objective weights based on the minimum deviation method.

Calculating subjective weights based on AHP
Analytic Hierarchy Process (AHP) is a hierarchical and systematic multi-objective and multi-criteria decision analysis method that combines qualitative and quantitative analysis.By applying the idea of system analysis, complex multi-objective and multi-criteria decision problems are transformed into simple quantitative decision problems.It has been widely used in the evaluation, prediction, system analysis, and other aspects.The main (1) Establishing a hierarchical structure model.The ultimate goal of this article was to evaluate the waterrichness of the clastic rock aquifer on the roof of the mining coal seam, and used this as the target layer (A layer); the lithological structural characteristics and structural development characteristics reflected the water-richness of the aquifer, but their impact needed to be reflected through specific factors related to them as the rule layer of the model (B layer); the specific main controlling factors included the depth of the sandstone floor, brittle rock ratio, lithological structure index, fault strength index, fault intersections and endpoints density, which constituted the decision layer of the model (C layer).The hierarchical structure model was shown in Fig. 7.
(2) Constructing a judgment matrix.Based on the varying degrees of influence of various main controlling factors on the evaluation of water-richness of sandstone aquifers, a quantitative analysis was conducted according to a certain scale to construct a judgment matrix.Collected the opinions of coal mine water prevention and control researchers and experts with rich on-site work experience in Huafeng mine field, and used the 1-9 scale method (Table 3) proposed by American operations researcher T.L. Satty 33 to score the importance of the two major factors in the rule layer and the five main controlling factors in the decision layer, and established corresponding judgment matrices.(3) Consistency checking.Performed a consistency proportion test on each judgment matrix, and only after passing the consistency test can the weights obtained from the judgment matrix be accepted.First, the consistency index CI of the n order judgment matrix was calculated by the following formula: where max is the maximum eigenvalue of judgment matrix.CI = 0 indicates that the judgment matrix is completely consistent, CI < 0.1, the judgment matrix and single ranking of intra layer factors conform to logical consistency; if CI > 0.1, the assignment of factor weights within the judgment matrix needs to be adjusted.
Then, the consistency ratio CR could be calculated by the following formula:  where RI is the judgment matrix average random consistency indicator.CR < 0.1, the consistency of the judgment matrix is considered within the allowable range, and the weight vector calculation can be performed using the eigenvectors of the judgment matrix.
(4) Obtaining the weight of the main control factor.Using the square root method to calculate weights, firstly calculated the n power of the product of each row of the n order judgment matrix to obtain an n vector.The vector factor calculation formula was as follows: where ω i is the I element of an n dimensional vector; a ij is the scale value of the I row and the j column; i,j = 1, 2, …, n.
Normalizing the n dimensional vector mentioned above was the weight vector, which could obtain the weight: where ω i is the weight value of the I main controlling factor.

Calculating objective weights based on rough set theory improved by conditional entropy
Rough Set Theory is a mathematical method for dealing with fuzziness and uncertainty 34 .It can mine potential and valuable knowledge from a large amount of data, reducing the unnecessary workload caused by redundant knowledge in calculation and classification.When processing data, there is no need to provide prior information beyond the data, and the importance of each attribute can be determined.Currently, it is widely used in objective weight calculation.In the process of calculating attribute weights using rough set theory, there may be situations where the weight of a certain attribute is 0. The reason for this phenomenon is that Rough Set Theory only considers the importance of a single attribute to the entire attribute set, without considering the importance of the attribute itself and neglecting the practical significance of the attribute 35 .To solve this problem, the concept of Conditional Entropy is introduced to improve the method of calculating attribute weights using Rough Set Theory.The objective weight calculation steps for the main controlling factors of water-richness of clastic rocks on the roof of the mining coal seam were as follows.
(1) The knowledge system S for data processing related to water-richness evaluation was established as follows: where U is a set of objects, also known as a universe; A = C ∪ D, C ∩ D = ∅, C is the set of conditional attributes, D is the set of decision attributes; V = U a∈A V a is a set of attribute values, V a represents the range of attribute values for attribute A, that is, the range of values for attribute a; f : U × A → V is an information function that specifies the attribute value of x for each object in U.
(2) Data standardization and classification.The selected controlling factors have different dimensions.To make the data more comparable and objective, the original data was standardized using the range standardization formula: where X is the original value of this indicator; X max , X min are the maximum and minimum values in the original data of the indicator, respectively, Xi is the standardized result value of this indicator.
(3) Reducing knowledge system data.In the decision table, if there were identical conditional attribute values and most of the decision attribute values were the same but differ, remove the few rows that caused the difference in the decision attributes and saved the rows with the same decision attribute values; If two rows with the same conditional attribute and different decision attribute values were encountered, these two rows could be deleted, as the sample had no specific significance for classification; If there were several rows in the policy table with consistent values for conditional attributes or decision attributes, then kept one of them 36 .
(4) Using Conditional Entropy to improve the Rough Set method for calculating attribute weights.a. Calculating the conditional entropy of decision attributes.In decision information table S = U, C, D, V , f , the conditional entropy of decision attribute set could be expressed as: ( 16) where New Sig(C i ) represents the degree of change in the attribute set after removing the conditional attribute C i , indicating the importance of the conditional attribute C i relative to the entire conditional attribute set.c.Calculating attribute weights.By comprehensively considering the above two aspects and standardizing them, the weights of each conditional attribute (factor) could be obtained: where I(D|C i ) indicates the importance of the conditional attribute C i itself in the system.
According to the above steps, the conditional entropy, importance, and weights of each main controlling factor could be obtained.

Calculating comprehensive weights based on the minimum deviation method
After calculating the subjective and objective weights using AHP and improved rough set theory, to balance the subjectivity and objectivity of the weight indicators and complement each other's strengths and weaknesses, a combination weighting method based on minimum deviation was adopted to fuse the subjective and objective weights, reduced the errors caused by a single weighting method, and obtained a more scientific and reasonable comprehensive weight 37,38 .
Assuming that decision-makers use a total of q methods to determine indicator weights, including subjective weighting method l and objective weighting method q-l, the weight vector is: In order to comprehensively consider the subjective opinions of decision-makers and the objectivity of decision-making, a deviation function is introduced to minimize the weight deviation obtained by various weighting methods, and ultimately obtain the weight vector w = {w 1 , w 2 , • • • , w m } T .The specific steps are as follows.
(1) Constructing a single objective optimization model: where a k is the weight coefficient corresponding to various weighting methods; a j is the weight corresponding to the j weighting method; f j (u k ) , g j (u k ) is the deviation function of subjective weighting method and objective weighting method, respectively.In order to fully utilize the weight information determined by various weighting methods, the weight deviation of each weighting method should be smaller.Therefore, the constructed model is: (2) Constructing the corresponding Lagrange function: where λ is an introduced parameter.
According to the necessary conditions for the existence of extreme values, there are: where L is the constructed Lagrange function.
According to Kramer's law, the coefficient determinant of the linear equation system is not 0, so the equation system has a unique solution, which is the corresponding weight coefficients of various weighting methods.By weighting them with the indicator weights of the corresponding methods, the final weight value can be obtained.
(3) Obtaining a system of comprehensive weighting equations.By substituting the weight values obtained from the two weighting methods into the Lagrange function mentioned above, the equation system for obtaining the comprehensive weighting can be obtained: (4) Obtaining comprehensive weights.Substituting the obtained subjective and objective weight, α * = (α 1 , α 2 ) could be obtained.The comprehensive weight calculation of the main controlling factors for water-richness evaluation in this article was as follows: where α 1 is the weight coefficient of subjective weight; α 2 is the weight coefficient of objective weight; u 1i is the subjective weight; u 2i is the objective weight.

Constructing a water-richness classification model based on unascertained measurement theory
The unknown measurement theory was introduced into the evaluation of the water-richness of the coal seam roof water-bearing layer.This theory satisfies the criteria of non-negativity, additivity, normalization, and temporality, and applies the principle of confidence.The advantage of the comprehensive evaluation model based on the measurement mathematics is that no useful information will be lost when making judgments, and the use of the provided confidence criteria will not result in unclear or unreasonable classifications as in the maximum membership principle, especially for the problem of ordered partition classes, the classification degree is more accurate and detailed 39 .The steps for constructing the evaluation model were as follows.
(1) Classifying evaluation indicators.When evaluating the target with an unascertained measure set, the key was constructing a reasonable unascertained measure function, and the first step was to establish a risk assessment level.On the basis of thorough research and analysis of the hydrogeological characteristics of the Huafeng mine field, a water-richness evaluation index for the study area was established through K-means clustering analysis and combined with the opinions of coal mine water prevention and control researchers, as shown in Table 4. Divided the waterrichness in the study area into four levels, namely strong water-richness (C4), relatively strong water-richness (C3), medium water-richness (C2), and relatively weak water-richness (C1).
(2) Constructing a single indicator measurement function.
Assuming there are n evaluation units in the aquifer to be evaluated, the space vector represents the quantitative value of the j evaluation indicator of the evaluation unit Q i , then the quantitative value of the evaluation indicator Q i of the evaluation unit Let α ijk = α X ij ∈ C k represent the degree to which the quantified value of the evaluation index belongs to the k evaluation level called an uncertain measure, abbreviated as a measure.A matrix α ijk m×s is called a single-index measure evaluation matrix, that is: According to the controlling factors and the characteristics of actual mining, this paper performed linear interpolation within the interval, that was, the idea of piecewise interpolation was used to insert linear points in each graded interval of the evaluation index.Based on the inserted points, a linear measure function was constructed as shown in Fig. 8.
(3) Constructing a comprehensive measure of multiple indicators based on indicator weights. Let represent the degree to which the evaluation unit Q i belongs to the k evaluation level C k .Then, the multi-index measure α ik = m j=1 ω j α ijk can be represented by a matrix as follows: (4) Grading through confidence recognition criteria.To obtain the final evaluation result of the evaluation unit, a "confidence degree" identification criterion is adopted for the grading evaluation of aquifer water abundance 40 .If R = (c 1 > c 2 > c 3 … > c z ), the evaluation space R is considered ordered.The confidence degree λ is introduced, where λ ≥ 0.5, and if can be regarded that the evaluation unit Qi belongs to the k 0 evaluation level C k0 .

Prediction of the development height of water-conducting fracture zones
(1) Empirical formulas The lithology of the roof strata of the 4th coal seam in the Huafeng mine field was analyzed, and different empirical formulas were used to calculate the development height of the waterconducting fractured zone based on the different roof lithologies.The predicted values using the empirical formula method were plotted using Golden Software Surfer software, as shown in Fig. 10a.(2) The GRNN model A total of 63 measured cases were collected and organized, forming a 63 × 5-dimensional raw data matrix (Table 5) (see the Supplementary Information 1).The selected four influencing factors were used as input parameters for the GRNN model, and the predicted values of the development height of the water-conducting fractured zone were used as output parameters.Since the number of layer parameters in the GRNN neural network model is equal to the number of input layers, and the number of summation layer parameters is one more than the output layer, the initial network structure of the GRNN neural network was designed as 4:4:2:1.Samples numbered 1 to 58 in the table were used as training samples, while samples numbered 59 to 63 were used as testing samples.The GRNN neural network model was trained using Matlab software, and the smoothing factor σ was adjusted to achieve the best fit of the training results.Finally, a GRNN neural network with a fitting degree of 0.9023 was obtained.
The coal seam thickness, proportion coefficient of hard rock lithology, dip length of the workface, and mining depth of the 4th coal seam in the Huafeng mine field were used as input parameters, and the developed GRNN model was utilized to predict the development height of the water-conducting fractured zone.The results were shown in Fig. 10b.
The predicted values of water-conducting fractured zone development height for the test samples obtained from the GRNN neural network method and empirical formula method were compared.The relative error of the two methods was shown in Fig. 9, and the average relative errors were 3.22% and 16.75%, respectively.The prediction accuracy of the GRNN neural network method was significantly higher than that of the empirical formula method.
The development height of the water-conducting fractured zone in the coal seam roof was calculated using the two aforementioned methods.The GRNN neural network method exhibited higher accuracy; however, prioritizing safety, the larger prediction value of the two methods was chosen as the final prediction value.A (33) 2.0000 0 0.0000 2.0000 0 0.0000 in the southwestern, central, and eastern parts of the study area.The relatively strong water-richness zone was present in small portions of the central and eastern parts of the study area.
Combined with the water inflow data and water inrush point records provided by the research area, the actual results were compared with the water abundance zoning model in this paper, as shown in Table 14.
Taking the water inrush data as an example, out of 7 water inrush points, 2 of them did not match the model zoning, resulting in an accuracy rate of 71.43% for the model.Taking the water inflow data from workfaces as an example, out of 13 workfaces, 2 of them did not match the model zoning for water inflow, while 9 of them matched the model zoning to a certain extent, resulting in an accuracy rate of 84.62% for the model.Overall, the accuracy rate of the water-richness zoning model in this study could reach 80%.

Conclusions
(1) The method combining the GRNN neural network with empirical formulas was employed to calculate the predicted values of the development height of the water-conducting fracture zone above the mined coal seam.The predicted values for the development height of the water-conducting fracture zone in the 4th coal seam roof of the Huafeng mine field ranged from 58 to 106 m.This range was determined to assess the vertical extent of water-richness evaluation.Through quantitative analysis, the degree of water hazard threat to the mined coal seam was determined, thereby improving the accuracy of evaluating the waterrichness of the clastic aquifer in the coal seam roof.(2) Depth of the sandstone floor, brittle rock ratio, lithological structure index, fault strength index, fault intersections and endpoints density were selected as the main controlling factors for water-richness in the study area, breaking away from the previous reliance on the unit water inflow factor.The method of the minimum deviation was introduced to optimize the combination of subjective weights obtained from the AHP and objective weights derived from the rough set theory improved by conditional entropy.This resulted in a combined weight that possesses the advantages of both subjective and objective weights.The combination weights for each main controlling factor are 0.1644, 0.267, 0.2111, 0.2215, and 0.136 in sequence.This significantly improves the reliability and accuracy of the weights, making the evaluation results more scientifically sound.(3) The theory of uncertain measurement was applied to the construction of a water-richness evaluation model by incorporating confidence identification criteria.The model was used to classify the water-richness of the clastic rock aquifer in the 4th coal seam roof of the Huafeng mine field.It was divided into relatively strong water-richness zones, medium water-richness zones, and relatively weak water-richness zones.By comparing the records of water inflow from workfaces and water inrush points within the study area, a www.nature.com/scientificreports/high degree of agreement was observed, reaching 80% accuracy.This validates the feasibility and accuracy of the proposed method in this study.

Figure 1 .
Figure 1.Structural outline map of Huafeng mine field.

Figure 9 .
Figure 9. Residual and relative error of different methods.

Figure 10 .
Figure 10.Predicted value of development height of water-conducting fracture zone.
ScaleRelative importance of two factors 1 Both factors are equally important 3 One factor is slightly more important than another 5 A certain factor is obviously more important 7 A certain factor is strongly more important 9 A certain factor is extremely more important 2, 4, 6, 8 The compromise value between the adjacent standards mentioned above Vol.:(0123456789)Scientific Reports | (2024) 14:6465 | https://doi.org/10.1038/s41598-024-57033-x . Calculating the importance of the condition attribute C i .In the decision information table, ∀Ci ∈ C , the importance of the conditional attribute C i could be expressed as: Scientific Reports | (2024) 14:6465 | https://doi.org/10.1038/s41598-024-57033-xwww.nature.com/scientificreports/b

Table 4 .
Evaluation indicators and grading standards.level evaluation, if it satisfies C 1 > C 2 > C 3 > … > C s , then {C 1 , C 2 , C 3 , …, C s } is called an ordered partition class of the level space R.

Table 5 .
Measured sample data of the height of the water-conducting fractured zone.

Table 6 .
Assessment of the main controlling factors.

Calculation of the weight values of the main controlling factors for water-richness (
1) Subjective weight.We invited a total of five researchers in coal mine water prevention and control and experts with rich on-site work experience in Huafeng mine field to evaluate and score the relative importance of the main controlling factors for water-richness of the clastic rock aquifer of the mining coal seam roof (Table6), and constructed a judgment matrix, as shown in Tables 7, 8 and 9. Conducted a consistency check on each judgment matrix, and the test results were shown in the table.The consistency ratio CR was

Table 10 .
Consistency check table for judgment matrix.

Table 11 .
Subjective weight of main controlling factors.

Table 12 .
Objective weight of main controlling factors.

Table 14 .
Validation between prediction results and actual data. No.